First-Order, Quasi-linear Equations and Method of Characteristics

Lokenath Debnath ()
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Lokenath Debnath: University of Texas, Pan American, Department of Mathematics

Chapter 3 in Nonlinear Partial Differential Equations for Scientists and Engineers, 2012, pp 201-226 from Springer

Abstract: Abstract Many problems in mathematical, physical, and engineering sciences deal with the formulation and the solution of first-order partial differential equations. From a mathematical point of view, first-order equations have the advantage of providing a conceptual basis that can be utilized for second-, third-, and higher-order equations. This chapter is concerned with first-order, quasi-linear and linear partial differential equations and their solutions by using the Lagrange method of characteristics and its generalizations.

Keywords: Quasi-linear Equations; First-order Partial Differential Equations; Independent Ordinary Differential Equations; Characteristic Direction Field; Three-dimensional Space Curve (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8265-1_3

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